References
- B. Ahmad and B. S. Alghamdi, Approximation of solutions of the nonlinear Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions, Computer Physics Communications, 179(6)(2008), 409-416. https://doi.org/10.1016/j.cpc.2008.04.008
- B. Ahmad, On the existence of T-periodic solutions for Duffing type integro-differential equations with p-Laplacian, Lobachevskii Journal of Mathematics, 29(1)(2008), 1-4. https://doi.org/10.1134/S1995080208010010
- A. Anguraj, M. Mallika Arjunan and E. Hernandez, Existence results for an impulsive partial neutral functional differential equations with state- dependent delay, Appl. Anal., 86(7)(2007), 861-872. https://doi.org/10.1080/00036810701354995
- A. Anguraj, S. Wu and A. Vinodkumar, Existence and Exponential Stability of Semilinear Functional Differential Equations with Random Impulses under Non-uniqueness, Nonlinear Anal. TMA, 74(2011), 331-342. https://doi.org/10.1016/j.na.2010.07.007
- A. Anguraj, A. Vinodkumar, Existence, Uniqueness and Stability Results of Random Impulsive Semilinear Differential Systems, Nonlinear Anal. Hybrid Syst. 4(3)(2010), 475-483. https://doi.org/10.1016/j.nahs.2009.11.004
- A. Anguraj, A.Vinodkumar, Existence and Uniqueness of Neutral Functional Differential Equations with Random Impulses, I. J. Nonlinear Sci., 8:4(2009), 412-418.
- T. A. Burton, Stability by Fixed Point Theory for Functional Differential Equations, Dover Publications, Inc., New York, 2006.
- M. Gowrisankar, P.Mohankumar, and A. Vinodkumar, Stability Results of Random Impulsive Semilinear Differential Equations, Acta Mathematica Scientia, 34B(4)(2014), 1055-1071.
- R. Haloi, Dwijendra N. Pandey, and D. Bahuguna, Existence and Uniqueness of a Solution for a Non-Autonomous Semilinear Integro-Differential Equation With Deviated Argument, Differ. Equ. Dyn. Syst., 20(1)(2012), 1-16. https://doi.org/10.1007/s12591-011-0099-x
- E. Hernandez, M. Rabello, and H.R.Henriquez, Existence of solutions for impulsive partial neutral functional differential equations, J. Math. Anal. Appl., 331(2007), 1135-1158. https://doi.org/10.1016/j.jmaa.2006.09.043
- D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. 27(1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
- R. Iwankievicz and S. R. K. Nielsen, Dynamic response of non-linear systems to Poisson distributed random impulses, Journal of Sound Vibration, 156(1992), 407-423. https://doi.org/10.1016/0022-460X(92)90736-H
- V. Lakshmikantham, D. D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
- X. Li, J. Wang, Ulam-Hyers-Rassias stability of semilinear differential equations with impulses, Electron. J. Diff. Equ., 2013(172)(2013), 1-8. https://doi.org/10.1186/1687-1847-2013-1
- A. M. Samoilenko, N.A Perestyuk., Impulsive Differential Equations, World Scientific, Singapore, 1995.
- J. M. Sanz-Serna and A. M. Stuart, Ergodicity of dissipative differential equations subject to random impulses, J. Diff. Eqns. 155(1999), 262-284. https://doi.org/10.1006/jdeq.1998.3594
- K. Tatsuyuki, K. Takashi and S. Satoshi, Drift motion of granules in chara cells induced by random impulses due to the myosinctininteraction, Physica A 248(1998), 21-27. https://doi.org/10.1016/S0378-4371(97)00455-X
- S. M. Ulam, A collection of mathematical problems, New York, Interscience Publishers, 1968.
- A. Vinodkumar, M. Gowrisankar, and P. Mohankumar, Existence, uniqueness and stability of random impulsive neutral partial differential equations, J. The Egyptian Mathematical Society, 23(2015), 31-36. https://doi.org/10.1016/j.joems.2014.01.005
- A. Vinodkumar, A. Anguraj, Existence of random impulsive abstract neutral non-autonomous differential inclusions with delays, Nonlinear Anal. Hybrid Syst. 5(2011), 413-426. https://doi.org/10.1016/j.nahs.2011.04.002
- A.Vinodkumar, Existence results on random impulsive semilinear functional differential inclusions with delays, Ann. Funct. Anal., 3(2)(2012), 89-106. https://doi.org/10.15352/afa/1399899934
- J. Wang, L. Lv, and Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, Electron. J. Qual. Theory Differ. Equ., 63(2011), 1-10.
- J. Wang, L. Lv, and Y. Zhou, New concepts and results in stability of fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 17(2012), 2530-2538. https://doi.org/10.1016/j.cnsns.2011.09.030
- J. Wang, Y. Zhou, and M. Feckan, Nonlinear impulsive problems for fractional differential equations and Ulam stability, Comput. Math. Appl., 64(2012), 3389-3405. https://doi.org/10.1016/j.camwa.2012.02.021
- J. Wang, M. Feckan, and Y. Zhou, Ulam's type stability of impulsive ordinary differential equations, J. Math. Anal. Appl., 395(2012), 258-264. https://doi.org/10.1016/j.jmaa.2012.05.040
- Wei Wei, Xuezhu Li, and Xia Li, New stability results for fractional integral equation,Comput. Math. Appl., 64(2012), 3468-3476. https://doi.org/10.1016/j.camwa.2012.02.057
- S. J. Wu, X. Z. Meng, Boundedness of nonlinear differential systems with impulsive effect on random moments, Acta Math. Appl. Sin., 20(1)(2004), 147-154. https://doi.org/10.1007/s10255-004-0157-z
- S. J. Wu, Y. R. Duan, Oscillation, stability, and boundedness of second-order differential systems with random impulses, Comput. Math. Appl., 49(9-10)(2005), 1375-1386. https://doi.org/10.1016/j.camwa.2004.12.009
- S. J. Wu, X. L. Guo and S. Q. Lin, Existence and uniqueness of solutions to random impulsive differential systems, Acta Math. Appl. Sin., 22(4)(2006), 595-600. https://doi.org/10.1007/s10114-005-0689-z
- S. J. Wu, X. L. Guo and Y. Zhou, p-moment stability of functional differential equations with random impulses, Comput. Mathe. Appl., 52(2006), 1683-1694. https://doi.org/10.1016/j.camwa.2006.04.026
- S. J. Wu, X. L. Guo and R.H. Zhai,Almost sure stability of functional differential equations with random impulses, DCDIS, Series A: Math. Anal., 15(2008), 403-415.
- Z. Yan, Nonlocal problems for delay integrodifferential equations in Banach spaces, Differ. Eqn. Appl., 2(1)(2010), 15-24.
- S. Zhang, J. Sun, Stability analysis of second-order differential systems with Erlang distribution random impulses, Advances in Difference Equations, 2013(4)(2013), 403-415.